MATHEMATICS HIGH SCHOOL

Multiple choicePoint M is the midpoint of segment QR. If QM = 2x + 5 and MR = 5x – 1, find the length of QR.

A) QR = 8
B) QR = -9
C) QR = 9
D) QR = 18

Answers

Answer 1

Answer:

Answer: choice D) 18

Explanation:

M is the midpoint of QR, so QM = MR, meaning that the two smaller pieces are equal (the two pieces combine back to QR)

Use substitution and isolate x

QM = MR

2x+5 = 5x-1

2x-5x = -1-5

-3x = -6

x = -6/(-3)

x = 2

If x = 2, then QM is

QM = 2x+5 = 2*2+5 = 9

and MR is

MR = 5x-1 = 5*2-1 = 9

both are 9 units long. Both are the same length as expected, so this helps confirm the answer.

The last thing we do is add up the two pieces QM and MR to get the length of QR. This is using the segment addition postulate.

QR = QM + MR

QR = 9 + 9

QR = 18

note: a negative length is never possible in any situation, so you can immediately eliminate choice B from the list of possible answers without even doing any math.

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How many trapezoids can you find in this grid of 12-points using four points as the vertices of a trapezoid?

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Can I see the graph?

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All parallelograms have 4 sides.

Answers

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3/7 of which is 2 1/14

Answers

Answer:

4 and 5/6; 29/6.

Step-by-step explanation:

3/7 of x is 2-1/14.

(3/7)x = 29/14

x = (29/14) * (7/3)

x = (29/2) * (1/3)

x = 29/6

3/7 of 4 and 5/6 is 2 1/14.

Hope this helps!

Answer:

29/6

TRUST ME IT'S RIGHT!

Write as a single term: sin(25°) cos(10°) − cos(25°) sin(10°).

Answers

Answer: cos (25° + 10°)

Step-by-step explanation: The expression:

sin(25°) cos(10°) − cos(25°) sin(10°)

is associated to the expression for the cosine of the sum of two angles that is:

cos (α+β) = sinα *cosβ -cosα*sinβ

Hence if we do α = 25° and β = 10°

by subtitution we get:

cos (25° + 10°) = sin(25°) cos(10°) − cos(25°) sin(10°)

PLEASE HELP!!!!!! Which expressions are equivalent to 1/81 ? Check all that apply.8^ -1

9^ -2

9^ 8/9^4

9^8/9^10

9^ -6 · 9^3

9^5 · 9^ -7

Answers

Answer:

$9^(-2)\n\n(9^(8))/(9^(10))\n\n9^(5)*9^(-7)$

Step-by-step explanation:

Let's evaluate the answers.

Think of numbers with negative exponents as numbers on the wrong side of the fraction. So if you have a negative exponent, you put it at the bottom of the fraction or up and then you remove the negative sign.

So let's take the first answer:

$9^(-2) \:is\:actually\:equal\:to\: (1)/(9^(2))\n\n(1)/(9^(2)) = (1)/(81)}$

Now the next one, according to the law of exponents, when dividing we subtract the exponents. (But this only applies if the coefficients are the same!)

$(m^(x))/(m^(y)) = m^(x-y)$

Applying this rule to the second answer:

$(9^(8))/(9^(10)) = 9^(8-10) = 9^(-2)=(1)/(9^(2)) = (1)/(81)$

The third one:

$9^5*9^(-7) = (9^5)/(9^(7)) = 9^(5-7) = 9^(-2) = (1)/(9^2) = (1)/(81)$

If you apply the same rules to the rest of the choices, you wil find that they are not equivalent to 1/81.

The expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

To determine which expressions are equivalent to 1/81, we can simplify each expression and check if it equals 1/81.

$8^(-1)$ : This expression is equivalent to 1/8, not 1/81. Therefore, it is not equivalent. $9^(-2)$ : This expression is equivalent to 1/9², which simplifies to 1/81. Therefore, it is equivalent to 1/81. $(9^8)/(9^4)$ : This expression simplifies to $9^((8-4)) = 9^4$ , which is not equal to 1/81. Therefore, it is not equivalent. $(9^8)/(9^(10))$ : This expression simplifies to $9^((8-10)) = 9^(-2)$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81. $9^((-6)) \cdot 9^3$ : This expression simplifies to $(1)/(9^6) \cdot 9^3 = 1/729$ . Therefore, it is not equivalent. $9^5 \cdot 9^((-7))$ : This expression simplifies to $9^((5-7)) = 9^((-2))$ , which is equivalent to 1/9². Therefore, it is equivalent to 1/81.

Thus, the expressions that are equivalent to 1/81 are $9^(-2)$ , $(9^8)/(9^(10))$ , and $9^5 \cdot 9^(-7)$ .

Learn more about the expression here :

brainly.com/question/21751419

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